Halfway through the Mavericks’ simply boffo Friday show at the Lincoln Theatre, uniformed officers stepped in to clear the aisles near the stage and send the mob of dancing 60-somethings up front back to their seats. The crowd was having too much fun.

Inciting fun is among the few constants in the Miami-based combo’s 30-year career, a milestone now being celebrated with a retrospective world tour. Brilliance from peerless, golden-voiced frontman Raul Malo is another.

After the cops broke up the blissful, AARP-friendly rowdies, Malo thanked longtime fans for standing by his band — despite its utter lack of commitment to any particular musical genre — adding that there’s no way to easily explain “what the hell we do” to anybody unfamiliar with the melding of country, salsa, polka, ska, rockabilly, ’50s pop and rock, all of which were delivered in heaping helpings on this night. That aural diversity may have kept the Mavericks off radio playlists throughout their long run, but since the sum of those parts is, again, tons of fun, the live shows have always drawn an audience.

The downtown theater had nary an empty seat.

During 1994’s Texas swing-ish nugget, “Losing Side of Me,” keyboardist and wacky hypeman Jerry Dale McFadden, decked out in a colorful scarf and suit in a louder shade of yellow than can be found on any mustard bottle, fired fans up with an assortment of dance moves as goofy as they’ve come to expect. Malo came to the stage decked out in a black dress shirt, mostly unbuttoned to show lots of chest and a giggly cool assortment of metal medallions. The gaudy garb seemed fitting, as he channeled Elvis Presley while reprising the breakthrough single, “What a Crying Shame.” On an extended version of “All Night Long,” Malo threw in some throaty, Louis Armstrong-like phrases and a couple of minutes of the Fifth Dimension chestnut, “Aquarius/Let the Sunshine In.” On “All Over Again,” Michael Guerra, an accordionist with great hair, traded solos with guitarist Eddie Perez, who has even greater hair and whose stage moves and twangy licks recall his mentor Dwight Yoakam.

The band has survived some tough stretches. The Mavericks went on hiatus in 2004, as Malo — with his otherworldly vocal gifts — took an inevitable shot at a solo career. A 2012 comeback was crimped by the reported addiction (to opiates) of original bassist Robert Reynolds. Reynolds’s marriage to Trisha Yearwood surely helped the Mavs get a foothold in Nashville early on, despite their noncommittal attitude toward strict country. (Yearwood left Reynolds long ago, ending up with Garth Brooks.) Reynolds was ultimately, and very publicly, fired in 2014, as the band directly blamed his dependence on narcotics for the dismissal.

But no buzz-killing fallout from those dark episodes was evident at any point in this show. Malo worked hard to get the crowd to expend whatever energy remained, with an encore that coupled the Mavericks’ own customary, Tejano-tinged closer, “All You Ever Do Is Bring Me Down,” with a surprisingly faithful and flat-out rocking version of the Beatles “Back in the U.S.S.R.” A flock of graybeards and their partners swarmed toward the stage and cut loose once more, and this time around, thankfully, the house lawmen let it be.